共查询到20条相似文献,搜索用时 31 毫秒
1.
The origins of kriging 总被引:30,自引:0,他引:30
Noel Cressie 《Mathematical Geology》1990,22(3):239-252
In this article, kriging is equated with spatial optimal linear prediction, where the unknown random-process mean is estimated with the best linear unbiased estimator. This allows early appearances of (spatial) prediction techniques to be assessed in terms of how close they came to kriging. 相似文献
2.
Kriging Prediction Intervals Based on Semiparametric Bootstrap 总被引:1,自引:0,他引:1
Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased
predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian
assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian,
even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric
bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process
are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method
works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods
relying on Gaussian assumptions. 相似文献
3.
Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around
the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health
risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for
entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil
pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method
for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data
observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK),
Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and
nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with
a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by
bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores. 相似文献
4.
The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets 总被引:5,自引:0,他引:5
Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference.
Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical
models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging
models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated
with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation
(in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting
its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form
may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably
calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based
models are useful in that they provide extra information on the spatial processes generating the data that are being predicted. 相似文献
5.
Masoomeh Delbari 《Arabian Journal of Geosciences》2014,7(10):4221-4233
This paper presents the incorporation of a digital elevation model into the spatial prediction of water table elevation in Mazandaran province (Iran) using a range of interpolation techniques. The multivariate methods used are: linear regression (LR), cokriging (COK), kriging with an external drift (KED) and regression kriging (RK). The analysis is performed on 3 years (1987, 1997 and 2007) of water table elevation data from about 260 monitoring wells. Prediction performances of the different algorithms are compared with two univariate techniques, i.e. inverse distance weighting and ordinary kriging (OK), through cross validation and examination of the consistency of the generated maps with the natural phenomena. Significantly smaller prediction errors are obtained for four multivariate algorithms but, in particular, KED and RK outperform LR and COK for 3 years. The results show the potential for using elevation for a more precise mapping of water table elevation. 相似文献
6.
Goovaerts P 《Mathematical Geosciences》2010,42(5):535-554
A common issue in spatial interpolation is the combination of data measured over different spatial supports. For example,
information available for mapping disease risk typically includes point data (e.g. patients’ and controls’ residence) and
aggregated data (e.g. socio-demographic and economic attributes recorded at the census track level). Similarly, soil measurements
at discrete locations in the field are often supplemented with choropleth maps (e.g. soil or geological maps) that model the
spatial distribution of soil attributes as the juxtaposition of polygons (areas) with constant values. This paper presents
a general formulation of kriging that allows the combination of both point and areal data through the use of area-to-area,
area-to-point, and point-to-point covariances in the kriging system. The procedure is illustrated using two data sets: (1)
geological map and heavy metal concentrations recorded in the topsoil of the Swiss Jura, and (2) incidence rates of late-stage
breast cancer diagnosis per census tract and location of patient residences for three counties in Michigan. In the second
case, the kriging system includes an error variance term derived according to the binomial distribution to account for varying
degree of reliability of incidence rates depending on the total number of cases recorded in those tracts. Except under the
binomial kriging framework, area-and-point (AAP) kriging ensures the coherence of the prediction so that the average of interpolated
values within each mapping unit is equal to the original areal datum. The relationships between binomial kriging, Poisson
kriging, and indicator kriging are discussed under different scenarios for the population size and spatial support. Sensitivity
analysis demonstrates the smaller smoothing and greater prediction accuracy of the new procedure over ordinary and traditional
residual kriging based on the assumption that the local mean is constant within each mapping unit. 相似文献
7.
Spatial prediction is a problem common to many disciplines. A simple application is the mapping of an attribute recorded at a set of points. Frequently a nonlinear functional of the observed variable is of interest, and this calls for nonlinear approaches to prediction. Nonlinear kriging methods, developed in recent years, endeavour to do so and additionally provide estimates of the distribution of the target quantity conditional on the observations. There are few empirical studies that validate the various forms of nonlinear kriging. This study compares linear and nonlinear kriging methods with respect to precision and their success in modelling prediction uncertainty. The methods were applied to a data set giving measurements of the topsoil concentrations of cobalt and copper at more than 3000 locations in the Border Region of Scotland. The data stem from a survey undertaken to identify places where these trace elements are deficient for livestock. The comparison was carried out by dividing the data set into calibration and validation sets. No clear differences between the precision of ordinary, lognormal, disjunctive, indicator, and model-based kriging were found, neither for linear nor for nonlinear target quantities. Linear kriging, supplemented with the assumption of normally distributed prediction errors, failed to model the conditional distribution of the marginally skewed data, whereas the nonlinear methods modelled the conditional distributions almost equally well. In our study the plug-in methods did not fare any worse than model-based kriging, which takes parameter uncertainty into account. 相似文献
8.
R. J. Yao J. S. Yang P. Gao H. B. Shao G. M. Liu S. P. Yu 《Environmental Earth Sciences》2014,71(1):233-243
Soil salinity has been known to be problematic to land productivity and environment in the lower Yellow River Delta due to the presence of a shallow, saline water table and marine sediments. Spatial information on soil salinity has gained increasing importance for the demand of management and sustainable utilization of arable land in this area. Apparent electrical conductivity, as measured by electromagnetic induction instrument in a fairly quick manner, has succeeded in mapping soil salinity and many other soil physical and chemical properties from field to regional scales. This was done based on the correlation that existed between apparent electrical conductivity and many other soil properties. In this paper, four spatial prediction methods, i.e., local polynomial, inverse distance weighed, ordinary kriging and universal kriging, were employed to estimate field-scale apparent electrical conductivity with the aid of an electromagnetic induction instrument (type EM38). The spatial patterns estimated by the four methods using EM38 survey datasets of various sample sizes were compared with those generated by each method using the entire sample size. Spatial similarity was evaluated using difference index (DI) between the maps created using various sample sizes (i.e., target maps) and the maps generated with the entire sample size (i.e., the reference map). The results indicated that universal kriging had the best performance owing to the inclusion of residuals and spatial detrending in the kriging system. DI showed that spatial similarity between the target and reference maps of apparent electrical conductivity decreased with the reduction in sample size for each prediction method. Under the same reduction in sample size, the method retaining the most spatial similarity was universal kriging, followed by ordinary kriging, inverse distance weighed, and local polynomial. Approximately, 70 % of total survey data essentially met the need for retaining 90 % details of the reference map for universal kriging and ordinary kriging methods. This conclusion was that OK and UK were two most appropriate methods for spatial estimation of apparent electrical conductivity as they were robust with the reduction in sample size. 相似文献
9.
Geostatistical Mapping with Continuous Moving Neighborhood 总被引:1,自引:0,他引:1
An issue that often arises in such GIS applications as digital elevation modeling (DEM) is how to create a continuous surface using a limited number of point observations. In hydrological applications, such as estimating drainage areas, direction of water flow is easier to detect from a smooth DEM than from a grid created using standard interpolation programs. Another reason for continuous mapping is esthetic; like a picture, a map should be visually appealing, and for some GIS users this is more important than map accuracy. There are many methods for local smoothing. Spline algorithms are usually used to create a continuous map, because they minimize curvature of the surface. Geostatistical models are commonly used approaches to spatial prediction and mapping in many scientific disciplines, but classical kriging models produce noncontinuous surfaces when local neighborhood is used. This motivated us to develop a continuous version of kriging. We propose a modification of kriging that produces continuous prediction and prediction standard error surfaces. The idea is to modify kriging systems so that data outside a specified distance from the prediction location have zero weights. We discuss simple kriging and conditional geostatistical simulation, models that essentially use information about mean value or trend surface. We also discuss how to modify ordinary and universal kriging models to produce continuous predictions, and limitations using the proposed models. 相似文献
10.
Multivariable spatial prediction 总被引:1,自引:0,他引:1
For spatial prediction, it has been usual to predict one variable at a time, with the predictor using data from the same type of variable (kriging) or using additional data from auxiliary variables (cokriging). Optimal predictors can be expressed in terms of covariance functions or variograms. In earth science applications, it is often desirable to predict the joint spatial abundance of variables. A review of cokriging shows that a new cross-variogram allows optimal prediction without any symmetry condition on the covariance function. A bivariate model shows that cokriging with previously used cross-variograms can result in inferior prediction. The simultaneous spatial prediction of several variables, based on the new cross-variogram, is then developed. Multivariable spatial prediction yields the mean-squared prediction error matrix, and so allows the construction of multivariate prediction regions. Relationships between cross-variograms, between single-variable and multivariable spatial prediction, and between generalized least squares estimation and spatial prediction are also given. 相似文献
11.
Block Kriging for Lognormal Spatial Processes 总被引:4,自引:0,他引:4
Noel Cressie 《Mathematical Geology》2006,38(4):413-443
Lognormal spatial data are common in mining and soil-science applications. Modeling the underlying spatial process as normal on the log scale is sensible; point kriging allows the whole region of interest to be mapped. However, mining and precision agriculture is carried out selectively and is based on block averages of the process on the original scale. Finding spatial predictions of the blocks assuming a lognormal spatial process has a long history in geostatistics. In this article, we make the case that a particular method for block prediction, overlooked in past times of low computing power, deserves to be reconsidered. In fact, for known mean, it is optimal. We also consider the predictor based on the “law” of permanence of lognormality. Mean squared prediction errors of both are derived and compared both theoretically and via simulation; the predictor based on the permanence-of-lognormality assumption is seen to be less efficient. Our methodology is applied to block kriging of phosphorus to guide precision-agriculture treatment of soil on Broom's Barn Farm, UK. 相似文献
12.
Jacques Rivoirard 《Mathematical Geology》2002,34(7):797-808
Kriging with external drift allows one to estimate a target variable, accounting for a densely sampled auxiliary variable. Contrary to cokriging, kriging with external drift does not make explicit the structural link between target variable and auxiliary variable, for the latter is considered to be deterministic. In this paper, we show that kriging with external drift assumes implicitly an absence of spatial dependence between the auxiliary variable and the residual of the linear regression of target variable on auxiliary variable at same point. This is the simple model with orthogonal residual, where cokriging is collocated and coincides with kriging of the residual. In this model, the cross-structure is proportional to the structure of the auxiliary variable, and the linear regression of target variable on auxiliary variable does not depend on the support. 相似文献
13.
The kriging update equations and their application to the selection of neighboring data 总被引:1,自引:0,他引:1
Xavier Emery 《Computational Geosciences》2009,13(3):269-280
A key problem in the application of kriging is the definition of a local neighborhood in which to search for the most relevant
data. A usual practice consists in selecting data close to the location targeted for prediction and, at the same time, distributed
as uniformly as possible around this location, in order to discard data conveying redundant information. This approach may
however not be optimal, insofar as it does not account for the data spatial correlation. To improve the kriging neighborhood
definition, we first examine the effect of including one or more data and present equations in order to quickly update the
kriging weights and kriging variances. These equations are then applied to design a stepwise selection algorithm that progressively
incorporates the most relevant data, i.e., the data that make the kriging variance decrease more. The proposed algorithm is
illustrated on a soil contamination dataset. 相似文献
14.
Chunfa Wu Jiaping Wu Yongming Luo Haibo Zhang Ying Teng Stephen D. DeGloria 《Environmental Earth Sciences》2011,63(5):1093-1103
It was not unusual in soil and environmental studies that the distribution of data is severely skewed with several high peak
values, which causes the difficulty for Kriging with data transformation to make a satisfied prediction. This paper tested
an approach that integrates kriging and triangular irregular network interpolation to make predictions. A data set consisting
of total Copper (Cu) concentrations of 147 soil samples, with a skewness of 4.64 and several high peak values, from a copper
smelting contaminated site in Zhejiang Province, China. The original data were partitioned into two parts. One represented
the holistic spatial variability, followed by lognormal distribution, and then was interpolated by lognormal ordinary kriging.
The other assumed to show the local variability of the area that near to high peak values, and triangular irregular network
interpolation was applied. These two predictions were integrated into one map. This map was assessed by comparing with rank-order
ordinary kriging and normal score ordinary kriging using another data set consisting of 54 soil samples of Cu in the same
region. According to the mean error and root mean square error, the approach integrating lognormal ordinary kriging and triangular
irregular network interpolation could make improved predictions over rank-order ordinary kriging and normal score ordinary
kriging for the severely skewed data with several high peak values. 相似文献
15.
Comparison of kriging techniques in a space-time context 总被引:1,自引:0,他引:1
Patrick Bogaert 《Mathematical Geology》1996,28(1):73-86
Space-time processes constitute a particular class, requiring suitable tools in order to predict values in time and space, such as a space-time variogram or covariance function. The space-time co-variance function is defined and linked to the Linear Model of Coregionalization under second-order space-time stationarity. Simple and ordinary space-time kriging systems are compared to simple and ordinary cokriging and their differences for unbiasedness conditions are underlined. The ordinary space-time kriging estimation then is applied to simulated data. Prediction variances and prediction errors are compared with those for ordinary kriging and cokriging under different unbiasedness conditions using a cross-validation. The results show that space-time kriging tend to produce lower prediction variances and prediction errors that kriging and cokriging. 相似文献
16.
《Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy》1999,24(3):261-268
Visualisation of seismic and tomographic results is a crucial point to properly understand the models provided by seismic methods. We consider several geostatistical methods (inverse distance weighting, point kriging and mathematical wavelets) to map surface wave tomography in a sparsely sampled study area, and to compare their accuracy and efficiency with proper raypath methodologies (inversion and projection onto convex sets). A large set of synthetic data is used to estimate seismic velocities before application to real data. The contour maps of prediction errors indicate that spatial prediction and inversion perform similarly. 相似文献
17.
G. Bourgault 《Mathematical Geology》1994,26(6):733-752
In geostatistics, factorial kriging is often proposed to filter noise. This filter is built from a linear model which is ideally suited to a Gaussian signal with additive independent noise. Robustness of the performance of factorial kriging is evaluated in less congenial situations. Three different types of noise are considered all perturbing a lognormally distributed signal. The first noise model is independent of the signal. The second noise model is heteroscedastic; its variance depends on the signal, yet noise and signal are uncorrelated. The third noise model is both heteroscedastic and linearly correlated with the signal. In ideal conditions, exhaustive sampling and additive independent noise, factorial kriging succeeds to reproduce the spatial patterns of high signal values. This score remains good in presence of heteroscedastic noise variance but falls quickly in presence of noise-to-signal correlation as soon as the sample becomes sparser. 相似文献
18.
A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These
transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study
presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured
transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity
maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and
ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated
data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates
to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother
than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even
natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic
information systems (GIS) as basic information for further groundwater study.
Received: 27 August 1999 · Accepted: 22 February 2000 相似文献
19.
Xavier Emery 《Mathematical Geology》2007,39(6):607-623
Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging.
In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random
field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant
over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the
random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian
random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended
to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for
conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging. 相似文献
20.
Compositional data are very common in the earth sciences. Nevertheless, little attention has been paid to the spatial interpolation of these data sets. Most interpolators do not necessarily satisfy the constant sum and nonnegativity constraints of compositional data, nor take spatial structure into account. Therefore, compositional kriging is introduced as a straightforward extension of ordinary kriging that complies with these constraints. In two case studies, the performance of compositional kriging is compared with that of the additive logratio-transform. In the first case study, compositional kriging yielded significantly more accurate predictions than the additive logratio-transform, while in the second case study the performances were comparable. 相似文献